I'm afraid your source is wrong.
The collocation get back from is not a three-word verb in either sense. Both are two-word verbs, and from is not a necessary part of the idiom but simply the head of a preposition phrase which expresses the origin or source.
The from piece is not merely separable but entirely detachable. In fact, that last example shows that you have to be very careful where you put it—this means something entirely different:
I got back everything that was stolen from the police.
In that position, the from piece means that the stuff in question was stolen from the police, not that you got it back from the police.
Ordinarily, you should consider only the collocation get back in deciding where your Direct Object should fall. If the DO’s a single pronoun it must follow the verb get.
I got it back.
If it’s a brief NP it usually follows the verb but may follow the particle back.
I got my book back.
I got back my book.
If it’s a ‘heavy’ (long) NP it should follow the particle.
I got back both the Rembrandts and three of the four Picassos.
However, if a source is specified with a from phrase even a very heavy DO should precede the particle; otherwise the from phrase arrives too abruptly at the end and it’s not immediately clear what it modifies:
DEPRECATED: I got back both the Rembrandts and three of the four Picassos from the thieves.
BETTER: I got both the Rembrandts and three of the four Picassos back from the thieves.